Key Takeaways
- Enter one recent race and you get your VDOT, equivalent times from 1500 m to the marathon, and training pace ranges. VDOT comes from the Daniels-Gilbert equations[1].
- The equivalent-times table sets Daniels next to Riegel[2]. For a 25:00 5K their marathons are 1:51 apart, and for a 45:00 10K 0:15, so the gap shows how much the choice of model matters for your input.
- Riegel's exponent is not fixed. The 1.06 that most calculators use is not one of the fits in his 1981 paper, so you can pick the paper's own values instead.
- A marathon time from a 5K or 10K assumes you are as well trained for 42 km as for the short race. Neither formula can see your long runs.
How the Calculator Works
Two published models run on the same race result.
| Result | How it is worked out | Basis |
|---|---|---|
| VDOT | The oxygen cost of your race pace, divided by the share of VO2max a runner can hold for that long | Daniels and Gilbert 1979[1] |
| Daniels equivalent time | The time at another distance that gives the same VDOT | Same equations, solved for time[1] |
| Riegel equivalent time | Your time × (new distance ÷ your distance) raised to the exponent | Riegel 1981[2] |
| Training pace ranges | The pace whose oxygen cost is a set share of your VDOT, using Daniels' published share ranges | V.O2 calculator ranges[3] |
What each result is and where it comes from. Source numbers match the sources list.
The two Daniels-Gilbert equations are the oxygen cost of running at a speed and the share of VO2max you can hold for a time[1]. Daniels and Gilbert built them from measured runners and race performances.
Worked example: a 25:00 5K
That is a pace of 5:00 per km and a VDOT of 38.3. The model assumes you were running at 94.0% of VO2max for those 25 minutes.
Daniels gives a marathon of 3:57:55. Riegel at 1.06 gives 3:59:47, which is 1:51 slower.
Equivalent Race Times: Daniels vs Riegel
Same input, two models, and the gap between them.
An equivalent time is what the same fitness is worth at another distance, if you were as well trained for it. It is not a forecast for race day.
Take a 45:00 10K. Daniels gives a half marathon of 1:39:44 and a marathon of 3:27:15. Riegel at 1.06 gives 1:39:17 and 3:27:01.
| Distance | Daniels | Riegel 1.06 |
|---|---|---|
| 1500 m | 5:54 | 6:01 |
| Mile | 6:22 | 6:29 |
| 3K | 12:36 | 12:34 |
| 5K | 21:42 | 21:35 |
| 10K | 45:00 | 45:00 |
| 15K | 1:09:16 | 1:09:10 |
| Half marathon | 1:39:44 | 1:39:17 |
| Marathon | 3:27:15 | 3:27:01 |
A 45:00 10K at every distance the calculator shows, from the calculator's own code.
Daniels notes that the closer the race is to the target distance, the better the prediction[1]. The page marks any target that is more than double or under half your distance with a dagger. That cutoff is my own rule, not a published one.
For a marathon, the safest input is a recent half marathon. If you only have a 5K, treat the marathon row as the best case. For paces over a distance you plan to race, see the marathon pace calculator and the running split calculator.
Which Riegel Exponent to Use
The usual 1.06 is a convention, not a measured constant.
Riegel fitted a power equation, time = a × distanceb, to records for about 3.5 to 230 minutes of effort[2]. The exponent b is his "fatigue factor": the higher it is, the faster pace falls as the distance grows.
His Table 1 gives different values for different groups, fitted to records up to 1 November 1979. The 1.06 that most calculators quote is not in that table[2]. He first published the formula in a 1977 Runner's World article[4].
| Exponent | Where it comes from |
|---|---|
| 1.06 | The commonly quoted value |
| 1.07732 | Men (world records) |
| 1.08283 | Women (world records) |
| 1.05352 | Men over 40 |
| 1.05374 | Men over 50 |
| 1.05603 | Men over 60 |
| 1.0637 | Men over 70 |
The running exponents in Riegel's 1981 Table 1, plus the commonly quoted 1.06.
The page defaults to 1.06 because that is what runners expect to see. A bigger exponent gives slower times at long distances, so try the world-record fit for your sex to see how much the answer moves.
These are fits to groups of fast runners, not to you. I found no source that says which exponent suits a recreational runner, so the choice is yours.
Training Pace Ranges
Derived from your VDOT, and labelled as derived.
The V.O2 calculator describes Easy running as roughly 59 to 74% of VO2max, Marathon pace 75 to 84%, Threshold 83 to 88% and Interval 97 to 100%[3]. The page turns each share of your VDOT into a pace with the oxygen cost equation.
Daniels prints single paces in his own tables, and I could not check mine against them. For a 25:00 5K, two calculators that cite his method show a threshold pace of 5:16 per km[6] and 5:17[5].
They show an interval pace of 4:45[6] and 4:41[5]. So treat the ranges as a guide to effort. There is no Repetition pace because I found no sourced range for it.
For a different pacing method built on a race result, see the Tinman running calculator or the Magic Mile calculator.
VDOT Is Not Your VO2max
It is a performance index that happens to be in the same units.
Daniels and Gilbert describe the reference value as a rough estimate of the VO2max that would allow the performance[1]. They add that it does not matter if it differs from a lab value, because performances still relate to each other accurately.
They name differences in how efficiently runners use oxygen as a cause of those gaps[1]. So two runners with the same lab VO2max can have different VDOTs. Use it to compare your own races, not to rank yourself against a lab number.
Accuracy and What It Cannot Tell You
Good for comparing races, weaker for predicting a specific day.
- It is not a forecast. Equivalent times assume equal training for each distance. A marathon from a 5K ignores your weekly mileage and long runs.
- Use an all-out race. A hard time trial or a race on a flat, measured course fits best. A jog or a hilly route will understate your VDOT.
- Weather, hills and altitude are not modelled. Heat, wind, a hilly course and altitude all slow a runner, and the page does not adjust for them.
- Riegel's range is limited. He fitted efforts of about 3.5 to 230 minutes[2]. Rows outside it carry a double dagger.
- Pace limits. The page accepts race paces from about 3:34 to 16:04 per mile and distances from 1500 m to the marathon. Those limits are mine, not published ones.
- No age or percentile ratings. Earlier versions of this page showed performance levels by age and sex, heart rate zones, running TSS and running economy. I removed them because I could not trace them to a source.
I tested the code against published worked examples: a 20:00 5K gives a VDOT of 49.8, and a 25:00 5K gives 38.3 with the equivalents shown on other VDOT calculators[5]. I did not test it against Daniels' printed book tables.
Frequently Asked Questions
Sources & References
- Oxygen Power: Performance Tables for Distance Runners (chapter reproduction, with the two regression equations). Daniels J, Gilbert J. Oxygen Power, 1979 (reproduced at vivamarathon.com) (1979)
- Athletic records and human endurance. Riegel PS. American Scientist 69(3):285-290 (1981)
- V.O.2 Running Calculator (training paces and their share of VO2max). Daniels J (V.O2). vdoto2.com
- Peter Riegel (secondary source, for the 1977 Runner's World article). Wikipedia. en.wikipedia.org
- VDOT Calculator: Training Paces & Race Times (secondary source, used as a cross-check of the 25:00 5K example). Vitadel. vitadel.com
- VDOT Calculator: Fitness Score & Equivalent Race Times (secondary source, used as a cross-check of equivalent times and paces). TrainPace. trainpace.com
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Disclaimer: This calculator is for informational and personal journaling purposes only. It logs measurements and compares them to published reference values. It is not health, medical, or nutrition advice.